Business Statistics TU Exam Paper 2071
Time: 3 hrs | Full Marks: 100 | Pass Marks: 35
Candidates are required to give their answer in their own words as far as practicable. The figures in the margin indicate full marks.
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Group A
Brief questions answer [10×2=20]
- What will be the value of median of a moderately asymmetrical distribution? If the mean and mode are 20 and 24 respectively.
- The difference between the upper quartile and lower quartile of a certain frequency distribution is 4 and their sum is 16. Calculate the quartile deviation and its coefficient.
- Differentiate between exclusive class and inclusive class. How can you change inclusive classes into exclusive?
- The average price and standard deviation of price of Mansuli rice per kg. for the last seven days in two markets M_{1} and M_{2} are recorded below:
Average price (Rs.) | S.D. of price (Rs.) | |
Market M_{1} | 90 | 7 |
7Market M_{1} | 94 | 6 |
Which market shows greater variation in price?
5. The standard deviation of a symmetrical distribution is 7. What must be the value of fourth moment about mean in order that the distribution be Mesokurtic?
6. The sum of the squares of the differences of ranks obtained from eight pairs of observations of X and Y variable is calculated as 6. Calculate the rank correlation coefficient between the variables.
7. In the following straight line trend equation of production (‘000 tons), the year of origin is considered as 2004.
Y=20+3.5X
Estimate the production for the year 2009.
8. From the information of prices and quantities of four commodities in the base year 1983 and current year 2984, the following results are obtained Σp_{0}q_{1}=184; Σp_{1}q_{0}=121; Σp_{1}q_{1}=192; Σp_{0}q_{0}=108 where p_{0}, p_{1}, q_{0} and q_{1} have their usual meaning. Calculate the price index by Fisher’s formula.
9. Out of 9 candidates, 6 men and 3 women apply for two vacancies of a manufacturing company, what is the probability that one man and one woman are selected in that vacancies?
10. From the following pay-off table, prepare regret table:
N_{1} | N_{1} | N_{3} | |
S_{1} | 200 | 50 | 40 |
S_{2} | 100 | 60 | 30 |
S_{3} | 40 | 30 | 10 |
Group B
Descriptive answer question:
Attempt any Five questions. [5×10=50]
11. Find graphically the minimum value of Z=40x20y
Subject to Constraints:
x + 2y > 2; 3x + y > 3; 4x + 3y > 6; x, y > o.
12. (1) Distinguish between primary and secondary data. How can you collect secondary data?
(2) A clothing store purchased 65% of the ready-made clothes from supplier S_{1} and 35% are from supplier S_{2}. The past record shows that the percentage of damaged clothes purchased from suppliers S_{1} and S_{2} are 2% and 5% respectively. If a ready-made cloth is drawn at random from the total purchase and found to be damaged. What is the probability that the damaged cloth is purchased from supplier S_{1}?
13.The combined mean and variance of salaries of 250 workers of city A city B are 560 and 5497 respectively. The mean and variance of the salaries of 150 workers of city B are 500 and 81 respectively. Find the variance of salary of workers of city A.
Read complete notes of Limitations of First law of Thermodynamics
14. From the data given below, fit a straight line trend by the method of least square. Also calculate the trend values.
Year | 2006 | 2007 | 2008 | 2009 | 2010 |
Profit (in Rs.’000) | 12 | 18 | 20 | 23 | 27 |
Also estimate the profit for the year 2012.
15. The three commodities C_{1} C_{2} and C_{3} are purchased and sold by the three persons A, B and C. Mr. A purchase 4 units of C_{3} and sells 3 units of C_{1} and 5 units of C_{2}. Mr. B purchase 3 units of C_{1} and sell 2 units of C_{2} and 1 units of C_{3}. Mr. C purchase 1 unit of C_{2} and sells 4 units of C_{1} and 6 units of C_{3}. In the purchase – sell process Mr. A suffered a loss of Rs.1,000; Mr. B earns no profit and Mr. C earns Rs.40,000. Find the prices per unit of these commodities by using matrix method.
16.(1) Find the numerical value of the following determinant by using properties
(2) A manufacturing company has 1000 employees. 10% of the employees earn less than Rs.500 per day, 200 earn between Rs.500 and Rs.999; 30% earn between Rs.1,000 and Rs.1,499; 250 employees earn between Rs.1,500 and 1,999 and rest earn Rs.2,000 and above. Calculate the suitable average wage. Give the reason for your choice of average.
Group C
Analytical answer questions
Attempt any TWO questions
17. From the following Bi-variable table, compute correlation coefficient between advertisement expenditure and sales revenue and test the significance of the result. Also estimate sales revenue when advertisement expenditure is Rs.400,000.
Advertisement | Sales revenue (in Rs.’000) | ||||
0-50 | 50-100 | 100-150 | 150-200 | 200-250 | |
0-40 | 12 | 6 | 8 | – | – |
40-80 | 2 | 18 | 4 | 5 | 1 |
80-120 | – | 8 | 10 | 2 | 4 |
120-160 | – | 1 | 10 | 2 | 1 |
160-200 | – | – | 1 | 2 | 3 |
18. Using the following information, examine whether time reversal test and factor tests are satisfied by Paasche’s and Fisher’s index number formula or not.
Commodity | Base Year | Current Year | ||
Price | Quantity | Price | Quantity | |
A | 10 | 6 | 12 | 10 |
B | 12 | 12 | 15 | 15 |
C | 15 | 25 | 18 | 30 |
D | 20 | 40 | 25 | 40 |
E | 13 | 17 | 20 | 15 |
Also mention the features of Fisher’s and Paasche’s method.
19. The asset structure of listed companies in Nepal is given below:
Asset (Rs. in millions) | No. of listed companies |
0-5 | 20 |
5-10 | 25 |
10-15 | 50 |
15-20 | 40 |
20-25 | 20 |
25-30 | 15 |
Total | 170 |
a. Compute the skewness and kurtosis of the asset distribution by using moment method.
b. Interpret the result of skewness and kurtosis.
c. Also calculate the coefficient of variation of asset distribution.
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